Which irrational number is between 14−−√ and 18−−√ ?(1 point) Responses 19−−√ start root 19 end root 10−−√ start root 10 end root 15−−√ start root 15 end root 13−−√

Answer 1

To determine which of the given options is an irrational number between \(\sqrt{14}\) and \(\sqrt{18}\), we first need to find the approximate values of \(\sqrt{14}\) and \(\sqrt{18}\):

1. \(\sqrt{14} \approx 3.74\)
2. \(\sqrt{18} \approx 4.24\)

Thus, we are looking for an irrational number between approximately 3.74 and 4.24.

Now, let's estimate the values of the given options:

1. \(\sqrt{19} \approx 4.36\) (too high)
2. \(\sqrt{10} \approx 3.16\) (too low)
3. \(\sqrt{15} \approx 3.87\) (within the range)
4. \(\sqrt{13} \approx 3.61\) (too low)

The only option that fits between \(\sqrt{14}\) and \(\sqrt{18}\) is \(\sqrt{15}\).

Therefore, the irrational number between \(\sqrt{14}\) and \(\sqrt{18}\) is \(\sqrt{15}\).